adm: can create/alter tables, views, procedures, etc
write: can insert and update tables inside the database, as well as execute procedures that will change data
read: can only run queries or execute procedures that will return data - created most for running reports or dashboards
task: internal user specifically to run automated tasks (like backups, SSIS packages or run procedures)
From this list, only write and read are listed on Access front-end.
To track user activity, I have a log procedure fired after record saving. This procedure save user, date/time, form name, field name, old and new value.
For your scenario, I think you can log activity on a local table and submit to online table on logout.